163 Hypernumbers 
Date: 12/15/04

Hypernumbers, Lent and Christmas.

Source: Quartum Organum by Krypton.

"All in all there have been 136 different dates on which the various Christian sects have celebrated the birth of Christ." Quartum Organum, p.639

"It is at this time (Christmas) when the sun's physical forces are at their minimum, that the earth's psychic forces are most vital." Quartum Organum, p.639

"The Christmas season, about forty days (Lent), is to the year what the Sabbath is to the week, a time for renewing the spirit." Quartum Organum, p.640

Christmas- "It is evident from the foregoing that this date and festival are not Christian but Pagan in origin." Quartum Organum, p.639

Easter/Eastre (Norse)/Ishtar (Babylonian) arrives each year on a different date, therefore it is not a birthday or anniversary." Quartum Organum, p.643

"Easter was celebrating an event in the world's creation. Lent, the "time and death of the seed". This seed is not Christ. Old English "Lencten", means spring. Go back far enough and you will find it means the spring of the world." Quartum Organum, p.644

Source: Consciousness and Reality by Muses and Young.
Dewey Decimal Number: 154.M9725c

The nature of hypernumbers can reveal the projection process... (and ) on the source of the hologram world or ordinary bodily experience....to be able to go between the image world and the source world at will (time travel). Charles Muses

Seven Kinds of Numbers Beyond Sqrt-1

From Consciousness and Reality:









Maps attention focus, intensity relevant to selectivity, conditioning, cuing and attention


Maps memory processes including transconscious memory



Relates to ecology, feedback, stability of sys, including their type of entropy (pos/neg/null/hyper) (i type)



Actualizing of potential of selfhood in self-transcendence. v4=w4 allowing transition to



oU8=ov=et (supertime of Milne cosmology.) Time is modified by affecting amount of available energy



Bears on the constant integration through time, characteristic of selfhood/individuality, differentiation processes of time or duration with respect to which changes occur. Motion

Easter Moon Phases

From Consciousness and Reality:

The timing of Easter as the first Sunday after the first full moon of spring....they..constantly make the error of supposing that the waxing moon is the spiritually more important part of the lunar cycle...on the contrary,

that the waning moon (returning to the sun) fortnight is synchronized with the dispension of the greatest spiritual power.

A Wiccan Correction

"According to Wiccan Philosophy, timing of rituals corresponds to moon phase. For example, building rituals (to add to one's power, ability, finances, etc.) should be done during a waxing moon. Rituals related to diminishing (uncrossing or undoing anything or related to black magic) should be done during the waxing (Correction: 12/18/04 "waning") moon." Cinthia Swanson


  • ...acceleration of evolutionary rate...using the nature of numbers (hypernumbers) particularly w which properties are:

  • When multiplied by itself successively (iteration) all the resulting numbers lie on a certain ellipse.
  • Numbers resulting from multiplying the square root of w by itself successively also lie on the same ellipse, exactly 12 distinct points being generated by both these processes.

Figure 1. Two Ellipse's Crossing at 90 Degrees With All Hypernumber Points.

  • ...(+w) (full line) relates to waxing lunar phase from crescent to complete (light and dark) disc (full and new moons).

  • (-w) (dotted line) relates to waning lunar phase. Key meditation times correspond approximately to the points of the arrows on the dotted line (-w) orbits = +/-sqrt-w. These two hypernumber orbits provide the only available mathematical paradigms...of the 3 principle irregularities in the lunar orbit known since Ptolemy, Kepler and Brahe...which together, furnish a set of 8 places...where these irregularities (reflecting configurations of forces) are maximal.

These 8 places map by the integer powers of (+w, -w) of Fig 1:

  • +/-1
  • +/-w
  • +/-(-1+w)
  • +/-(-1-w)

In terms of lunar phases the two points occur approximately two days less four hours, after full moon...

Session 1-10: 10 sessions per month:

10 lunar phases correspond to:

  • (+w)5   (-w)3
  • (-w)0   -sqrt-w
  • sqrt-w   (-w)4
  • (-w)    (-w)5
  • (-w)2   (-w)6

Sqrt-1 or i, no longer follows the associative rules of arithmetic (Hamilton).

  • 24 fundamental units of non-associative algebra.
  • Every number has a finite reciprocal.
  • 240 units of Cayley-Graves algebra were isomorphic with centers of 240 equal 8-dimensional spheres packed around a central 8-dimensional sphere.
  • 24 Hamiltonian units were isomorphic to centers of 24 equal 4-dimension spheres packed around a central 4-dimensional sphere.


e (in matrix form) appears in:

  • The Pauli spin operators.
  • The Dirac spinors.
  • The projection operators.
  • The neutrino operators.
  • The proper square roots of zero (Dirac Quantum Field Theory).

First 3 hyperforms of Sqrt+1

  • e1   e, e2 = -13   i, i2, i3 (Hamiltonian quaternerion elements).
  • e2   e2, e3 = -11
  • e3   e3, e1 = -12

U1, U2, U3

  • +/-1 is axis r or U1 -- e or i (Fractional dimension).
  • Sqrt-1 is   i or U2 -- Sqrt-1 (Negative dimension).
  • Sqrt+1 is   e or U3 -- U2 is approx. Sqrt-1 (genus). sphere = genus 0, donut = genus 1.


  • - (minus infinity).............................)
  • (bar) (anti-infinity).......................-(bar)
  • Fig 1A, 1B and 1C. For each kind of number there is a anti-number.

U7, w

Fig 1A.

U1 to U8

  • To harmonize Fig 1A with Fig. 1B, a 7 dimensional metaspace, curved in a flat 8-space, is required. 1A and 1B are two views of the same metasolid.

  • In terms of cosmology (which the hypernumbers map) the velocity of wave energy slows/approaches 0 at the cusp. Time, to perform the same task, infinitely expands, (to keep Planck's action, energy x time, a constant), thus the cusp is a unbridgeable barrier to any direct effort to cross it.

  • The shared w and v axis (central circle, Fig 1B) and its intersection with other (hyper) numbers occur at 0 (zero) and infinity. Those mutually perpendicular (hyper) number units (Un) whose axis' have thorn-like cusps (Fig. 1A) at +/-Un log are:


  • U1 (r) = unit of 1 of the axis of ordinary numbers.


  • U2 (i)(elemental) i.e., uncompounded and non-composite sqrt of the negative unit (+sqrt-1 or i)


  • U3 (e), not +1


  • U4 (p), proper elemental square root of 0.


  • U5 ( ), proper elemental infinite root of 0, it has the right/left hand Cornu spirals for its power orbit.


  • U6 (m), a complete system of Cassinian ovals for its power orbit.

  • The logarithms of infinity ( log ) and of 0 ( log 0 = -log ) are, respectively, the positive/negative forms of the lowest or zeroth order of infinities. Forming the two sharp cusps above and below in Fig. 1B. Only orbit U (v) can negotiate from 0 to 0(bar) without meeting the cusp or discontinuity (Fig. 1A).

  • v, w share the same axis but are different orbits.
    v is the counterpart of negative entropy.
    w is needed to reach v.

Fig. 1C

U7 (w), U8, U9 (v), v

U7 (w)

  • The unit power orbits of (U7) w are the perpendicular ellipses given by x2+/-xy + y2 = 1. In Cartesian form the orbit of (U9) consists of 4 comet-like curves whose Cartesian equation is y = +/- (x4+/- sqrt x2 - 1/x2) with x (axis of ordinary numbers) any y = v axis shared by w.

U9 (v)

  • At infinity, four U9 (v) curves join at point x = 0, y = ov.


Power of w.

  • In Physics, w, enters fundamentally into the vast differences found by quantum physics, to exist between observed and pre-observed particles. Observation or awareness changes the complexion of world probabilities.

Note: For proper results should the observation be positive, negative or neutral? MP

  • ...the real powers of w (that is, wk, where k is any positive or negative number) lie on an ellipse in the w-plane with center at 0 and with major axis along the diagonal running from the upper left to lower right; the intercepts on the w-axis and on the real axis are, respectively, +/-w and +/-1. The Cartesian equation of this ellipse is x2 + y2 + xy = 1, and thus the absolute value of every power of w is unity. Thus the square root of w is (1 + w / sqrt3), the absolute value of which is:

  • (1 + w / sqrt3)2 + (1 + w / sqrt3)2 + (1 + w / sqrt3)2 = 1.


  • In general, the absolute value of wk(= a + bw) is +sqrt a2 + b2 + ab. The natural logarithm of w is given very appropriately by -0.6 + 1.18w. From the remarkable characteristic properties:

  • w2 = -1 + w   (-w)2 = -1 + (-w)
  • w3 = -1      (-w)3 = -1
  • w4 = -(w)    (-w)4 = -(-w) = w
  • w5 = 1-(w)   (-w)5 = 1-(-w)
  • w0 = w6 = 1   (-w)0 = (-w)6 = 1

  • For ordinary numbers and some types of higher numbers (-x)2 = x2. For w this is not so. Thus:

  • (-w)2 = -1-w }
  • w2 }
  • -(-w) and +w or +(-w) and -(+w) are not in the same context of multiplication.
  • For ordinary numbers -(-x) is always x. And +(-x) and (-x) are both x.


  • The Cartesian equation of the (-w) ellipse is x2 + y2 - xy = 1; the value of w(-w) is always decidable from context.

The (U2) i-circle and (U7) w-ellipses

  • There is an important relationship between i and w.
    Power orbits i = circle. x2 + y2 = 1
              w = ellipse. x2 + xy + y2 = 1

  • The difference between i and w:
    -i has the same power orbit as +i,
    -w is given by x2 - xy + y2 = 1, an ellipse whose major and minor axis are respectively perpendicular to those of the +w ellipse.
    i and w are both perpendicular to each other and to the axis of ordinary numbers. The power orbit of k(+/-i) given by circle x2 + y2 = k2.
    The power orbit of k(+/-w) given by ellipse x2 +/-xy + y2 = k2.


  • The eccentricity of the pair of w-ellipses is sqrt2 / sqrt3 or slightly less than 0.8164 and,

Note: The 2/3 ratio shows up here as sqrt.

  • The projective or eccentric angle of arc tan sqrt2, or slightly less than 54 degrees 44'.

Note: 54 degrees 44' is a Buckminster Fuller angle.

  • These are the only ellipses, w, that can generate hypernumber orbits.

Consciousness and Reality by Muses and Young.
Dewey Decimal Number: 154.M9725c